Proceedings of the Workshop on

Special Geometric Structures in String Theory

Bonn, 8th-11th September, 2001

Preface

Manifolds with special geometric structures, such as
special Kähler, hyper-Kähler and quaternionic-Kähler
manifolds play a prominent role in string theory.
These structures occur as natural structures on certain moduli spaces or
on target spaces of low energy effective limits of string theories.
For example it is well known that supersymmetry
requires various target spaces (for sigma models, scalar fields in
supergravity theories, etc.) to have certain special geometric
properties. In many cases these requirements have
interpretation as restrictions on the holonomy group of the Riemannian
target space metric. However, in some cases, they cannot be expressed
in terms of the Riemannian holonomy group alone and give rise to new
geometries previously unknown to mathematicians.
Special Kähler manifolds, for instance, which arose in the
pioneering papers of de Wit and Van Proeyen, play a crucial
role as admissible target spaces for scalar
and vector couplings in both rigid and local N=2 supersymmetric theories
with vector multiplets. Other developments
involving special Kähler geometry are Seiberg-Witten duality
and the AdS/CFT correspondence. The latter provided further applications
of special geometries, including the appearance of five-dimensional variants,
very special manifolds, of relevance for brane-world scenarios.

The above topics, from both mathematical as well as physical perspectives,
were the focus of this workshop held in Bonn between 8th and
11th September, 2001, under the auspices of the
DFG (German Science Foundation) priority programme in
String Theory .
Other topics included spinor geometry, geometries with torsion
and Yang-Mills theory.
The idea of the workshop was to promote dialogue across
the interdisciplinary boundary by bringing together physicists and mathematicians
working on areas of mutual interest. Eighteen talks were held
(see the programme ). Nine of these
appear in these proceedings.